Abstract

In general, projective transformations of a plane vary shape, spacing [ D. L. MacAdam, J. Opt. Soc. Am. 32, 2– 6 ( 1942)] and angles of plane figures which are uniquely defined in the affine sense corresponding to general usage. Projective transformations may also transform points inside a figure into points outside the transformation of the figure, if one considers the original and transformed figure in the affine sense. If all interior points of a figure are transformed to interior points of the transformed figure, then the transformation is said to be invariant with respect to insidedness of that figure.

The purpose of this paper is to derive the condition under which the projective transformations of the Maxwell triangle are invariant with regard to insidedness. The meaning of this condition is illustrated by an example violating this condition, namely, a transformation of the CIE (x,y) diagram such that the confusion lines of the protanope and tritanope are respectively parallel to either coordinate axis.

© 1954 Optical Society of America

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